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N-detachable pairs in 3-connected matroids I: Unveiling X
Journal of Combinatorial Theory Series B ( IF 1.4 ) Pub Date : 2019-09-02 , DOI: 10.1016/j.jctb.2019.08.005
Nick Brettell , Geoff Whittle , Alan Williams

Let M be a 3-connected matroid, and let N be a 3-connected minor of M. We say that a pair {x1,x2}E(M) is N-detachable if one of the matroids M/x1/x2 or M\x1\x2 is both 3-connected and has an N-minor. This is the first in a series of three papers where we describe the structures that arise when M has no N-detachable pairs. In this paper, we prove that if no N-detachable pair can be found in M, then either M has a 3-separating set, which we call X, with certain strong structural properties, or M has one of three particular 3-separators that can appear in a matroid with no N-detachable pairs.



中文翻译:

3个连接的拟阵中的N个可分离对I:展开X

M为3个连接的拟阵,令NM的3个连接的未成年人。我们说一对{X1个X2}Ë中号如果拟阵之一是N可拆卸中号/X1个/X2 要么 中号\X1个\X2都是3连的,并且N负。这是三篇论文系列中的第一篇,我们描述了当M没有N个可分离对时出现的结构。在本文中,我们证明,如果在M中找不到N可分离对,则M具有3个分离集(我们称X为具有某些强结构特性),或者M具有3个特定的3个分隔符之一可以出现在没有N个可分离对的拟阵中。

更新日期:2019-09-02
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